Talk:Euler's three-body problem
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References needed
editNeeds references Doidimais Brasil 01:27, 11 July 2006 (UTC).
Especially for the `euler' part; i've never ever seen it called that.
Disambiguation
editThe Euler integral is not in the same coordinates... —Preceding unsigned comment added by 201.141.234.10 (talk) 04:15, 13 November 2007 (UTC)
Quantum Mechanical Description
editThat section was actually empty until I just added some material. The quantum version is harder than the classical version. Nonetheless, I thought it worthwhile to mention that some breakthrough was achieved for the Hydrogen molecule-ion: the energy eigenvalues are a generalization of the Lambert W function. —Preceding unsigned comment added by 24.6.171.96 (talk) 22:05, 19 January 2009 (UTC)
Simplicity
editCould someone start this off with a very simple description paragraph about what it is we're discussing? Or maybe create a topic on simple.wikipedia.org? —Preceding unsigned comment added by Bill Kress (talk • contribs) 17:16, 22 July 2009 (UTC)
- I agree, had a hard time understanding what this was about from the intro. Article getting looked up due to popular culture reference here: http://xkcd.com/613/ --Stéphane Charette (talk) 23:15, 22 July 2009 (UTC)
Euler: Archive, Translation, Demonstration
editThere should be a reference to the "Euler Archive" - use Google. 94.30.84.71 (talk) 21:37, 1 March 2012 (UTC)
Dr J R Stockton has in euler327.htm a rough translation of E.327 "De motu rectilineo trium corporum se mutuo attrahentium" (note the "rectilineo"); the Archive only has the original. He also has a demonstration of the constant-pattern solutions, for three bodies each of any mass and for any conic-section motion including degenerate cases. 94.30.84.71 (talk) 21:37, 1 March 2012 (UTC)
Links to Euler papers
editEuler wrote a great deal. Whenever any of his works are referred to, it would be well to give a link to the corresponding information page of the Euler Archive, which will link to the original and maybe to translations. The URL of such a link will be of the form http://eulerarchive.maa.org/pages/E337.html. 94.30.84.71 (talk) 12:44, 1 August 2012 (UTC)
Two massive bodies: fixed vs. circular motion
editThe article says that Euler's problem is solvable in closed form, and that the two massive may be fixed or moving in circles around the common barycenter (as in the circular restricted three-body problem). However, it is not clear for me that the second case is solvable in closed form. If that was the case, it would be easy to prove that equilibrium at the Lagrangian points L4 and L5 is Lyapunov stable.
According to another source that I checked, [1] the massive particles involved on Euler's problem are fixed.
I'll edit to eliminate the moving case. (Marcosaedro (talk) 19:28, 26 September 2012 (UTC))
Second constant of motion
editThe expression for the second constant of motion in the Euler's problem was taken from the cited Whittaker's textbook where it apparently contains a typo. I checked it by hand and found that there must be opposite signs in two last terms. I ask experienced participants to check it independently. TheGrysha (talk) 18:07, 13 March 2024 (UTC)